The DECI-Pizza Company has a special pizza that has 10 slices. Two of the

slices are each ‡ of the whole pizza, two are each , four are each ‡, and two are
each
24. A group of n friends share the pizza by distributing all of these slices.

They do not cut any of the slices. Each of the n friends receives, in total, an

equal fraction of the whole pizza. For what values of n > 1 is this possible?

To solve this problem, let's break down the pizza's slices and calculate the total fraction of the pizza they represent, and then determine for which values of \( n > 1 \) the pizza can be divided equally.

### Step 1: Break Down the Slices
The problem mentions four types of slices with no explicit fractions given for some of them. Let's use variables to represent the unknowns for now. We have:

- Two slices are each \(\frac{a}{b}\) of the whole pizza.
- Two slices are each \(\frac{c}{d}\) of the whole pizza.
- Four slices are each \(\frac{e}{f}\) of the whole pizza.
- Two slices are each \(\frac{g}{h}\) of the whole pizza.

### Step 2: Total Fraction of the Pizza
The total pizza is 1 whole pizza. Therefore, the sum of all slices should equal 1. The total fraction of the pizza is given by:

\[
2 \times \frac{a}{b} + 2 \times \frac{c}{d} + 4 \times \frac{e}{f} + 2 \times \frac{g}{h} = 1
\]

### Step 3: Conditions for Equal Distribution
We need to find the values of \( n > 1 \) for which each of the \( n \) friends can receive an equal share of the pizza without cutting any slices. This means that the total fraction each person gets is \( \frac{1}{n} \), and each person must receive a combination of slices that sums to \( \frac{1}{n} \).

The key to solving this is finding the values of \( n \) such that the total fraction 1 can be divided evenly into \( n \) equal parts, each part being \( \frac{1}{n} \).

Would you like me to solve for these variables or clarify any part of the breakdown?

The DECI-Pizza Company has a special pizza that has 10 slices. Two of the slices are each ‡ of the whole pizza, two are each , four are each ‡, and two are each 24. A group of n friends share the pizza by distributing all of these slices. They do not cut any of the slices. Each of the n friends receives, in total, an equal fraction of the whole pizza. For what values of n > 1 is this possible?

This problem explores how to equally distribute a pizza with various fraction-sized slices among n friends. It involves key mathematical concepts such as fractions, division, and equation solving. Suitable for students in Grades 7-10, this problem challenges learners to apply fraction arithmetic and solve for possible values of n.

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